Calculate element Z_i,j — Zij • LMDIR

There are many special cases for calculating the i,jth term in Z. These special cases must be handled on a term-by term basis. This function handles all those cases. See Z_byname() for details. The X matrices must be same size, must have same row and column names, and must have same row and column types. Note that i and j must be positive and less than or equal to nrow(X) and ncol(X), respectively.

Zij(
  i = NULL,
  j = NULL,
  X_0 = NULL,
  X_T = NULL,
  v_0i1 = matsbyname::rowprods_byname(X_0)[i, 1],
  v_Ti1 = matsbyname::rowprods_byname(X_T)[i, 1],
  X_0ij = X_0[i, j],
  X_Tij = X_T[i, j]
)

Arguments

i	optional row index for `X_0` and `X_T`.
j	optional column index for `X_0` and `X_T`.
X_0	optional sub-sector by factor matrix for time 0.
X_T	optional sub-sector by factor matrix for time T.
v_0i1	the i,1th element of the `v_0` column vector. (v_0 is formed from the row products of the `X_0` matrix.)
v_Ti1	the i,1th element of the `v_T` column vector. (v_T is formed from the row products of the `X_T` matrix.)
X_0ij	the i,jth element of the `X_0` matrix
X_Tij	the i,jth element of the `X_T` matrix

Value

the Z value corresponding to the v_0i1, v_Ti1, X_0ij, and X_Tij values

Details

Arguments i, j, X_0, and X_T are optional. If they are not specified, arguments v_0i1, v_Ti1, X_0ij, and X_Tij must be given.